0.999...

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「0.くっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっくっ・・・」
〜 0.999... について、如月千早

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概要

0.999...は、正確には 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 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99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999998999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999...もうやめていいですか？

数学的な性質

• 1と等しい
• 9を増やせば増やすほど1と等しくなる

1と等しいことの証明

${\begin{aligned}1-0.999...&=0.000...\\1-0.999...&=0\\1&=0.999...\\\end{aligned}}$

1から0.999...を引くと0.000...と無限に続く数字の最後に1がつく数になる。

無限に続くのだから最後がなく、1をつける場所が無く、小数点以下の0を省略できる。

両辺に0.999...を足すとこうなり、証明ができた。

また、

0.999...=x

とすると、

2x=1.999...

となる。

2x-x=x

1.999...-0.999...=1

ということは、

x=1

8行上の式と重ねると、

x=1=0.999...

やはり、1=0.999...である。

もっと確実な証明が必要な頭の堅い方はウィキペディアの0.999...へどうぞ。

0.999...を利用した計算式

1で済むのにわざわざ0.999...を使うバカはいねぇよ！しいて言えば

0.999...=1

だ！

0.999...の使い道

1を使えばいいだろ。というか、これを使用している人間は1と等しい事を知らないバカだけだろ……と言いたいところだが、一部で1を使用せずに0.999...を使用している例がある。

結婚式など

1は一桁で終わってしまうため、夫婦生活がすぐに終わってしまうことを連想させる。そのため、数学的に1と等しく、無限に桁がある0.999...が使用される。

余命など

例えば病院などで「余命1年でしょう」とか「1年もつか分かりません」と診断されると絶望的であるが「余命0.99999999...」と言えば無限に広がる夢が連想され、患者への精神的苦痛をおさえることができる。

ウィキペディアで使われている0.999...

0.999... - Wikipedia

何のためか分からないが、わざわざ右のような画像を使用してまで0.999...について説明しようとしている。まあ、このページも似たようなもんだが。

大学の数学

いちおー、大学の数学では0.999...は対角線論法という手法を通じて、自然数と実数の濃度（大きさのようなもの）が違うという証明をする際に使用する。0.999...を認めたくない学者は、この対角線論法をも攻撃する傾向がある。まったくもって、粘着質だ！ネチネチ。

0.999...を使えない場所・時

以下の場所・状況で1の代わりに0.999...を使用するとひよこ陛下に怒られ、殴られる。

葬式

0.999...は桁が無限に続く数字であるため、次々に死人が出ることや永遠に成仏できないことを連想させる。

1

ここでは1について説明しているため、0.999...は用無しである。ここの1を0.999...に置き換えると神や魔法使いに怒られるばかりでなく、アンサイクロペディアンとしての存在を抹消される。

0.999...の需要

上の計算式と使い道を見ればわかるように、需要はほとんどなし。上記以外の使い方をしたきみは勇気の塊であり究極のバカだ！

覚え方

「れいてんくっくっくっくっくっくっ…」の語呂合わせを使えば簡単に覚えられる。

ちなみに、円周率は、小数第500億位ぐらいまで覚えるとギネスブックに載るけど、0.999...は、いくら先まで覚えてもギネスとして認定されない。これをギネス記録だと認めてくれる心の優しい人はﾈ申になる。

関連項目

• 下記以外の数の一覧
  • 0 1 2 3 4 5 6 7 8 9
  • 10 11 12 13 14 15 16 17 18 19
  • 20 21 22 23 24 25 26 27 28 29
  • -4.001 -3.001 -2.001 -1.001 -0.001 0.999... 1.999 2.999 3.999 4.999 5.999
  • 30 40 50 60 70 80 90 100
  • 111 222 333 444 555 666 777 888 999 1000
  • 39 42 56 69 72 98 99 108 129.3 156 175 801 3594
  • 不可思議 無量大数 グーゴル 不可説不可説転 グーゴルプレックス
  • グラハム数 絶対値 二進数 十六進数 ロンギヌス数
  • -0.999...
  • 1/0.999...

• 西暦：0.999...年 紀元前0.999...年 0.999...世紀
• 0.999...cm
• 国道0.999...号
• 1=2
• 無量対数 - この数字の9の数は無量対数個以上ある
• 0.999...=1? - ウィキペディアの数学に対しての批判がある
• ゼノン_(エレア派) - 素人には論破不可能と思える高度な詭弁を弄する人物。しかしちょっと考えてみれば、彼の詭弁は「0.999...=無限大」というあり得ない仮定が根拠となっているのがわかる。「0.999...=1」だという事実を突きつける事によって論破可能である。

この項目「0.999...」は、内容が足りません。このままでは驚くべき証明を書く余白が残ってしまいます。内容を充実させてくれる人を探しています。 (Portal:スタブ)